Question

$49x - 57y = 172 and 57x - 49y = 252$
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Answer 1

Topic :-

• Linear Equation in Two Variable

Given :-

• 49x - 57y = 172 . . . .equation (1)
• 57x - 49y = 252 . . . . equation (2)

To Find :-

• Value of 'x' and 'y'.

Solution :-

Adding equation (1) and (2) :-

(49x - 57y) + (57x - 49y) = 172 + 252

Opening brackets,

49x - 57y + 57x - 49y = 172 + 252

Grouping similar terms,

(49x + 57x) + (-57y - 49y) = 172 + 252

Solving further,

106x + (-106y) = 424

106x - 106y = 424

106(x - y) = 424

x - y = 424/106

x - y = 4 . . . . equation (3)

Subtracting equation (1) from (2) :-

(57x - 49y) - (49x - 57y) = 252 - 172

Opening brackets,

57x - 49y - 49x + 57y = 252 - 172

Grouping similar terms,

(57x - 49x) + (57y - 49y) = 252 - 172

Solving further,

8x + 8y = 80

8(x + y) = 80

(x + y) = 80/8

x + y = 10 . . . . . equation (4)

Adding equation (3) and (4) :-

(x - y) + (x + y) = 4 + 10

Opening brackets,

x - y + x + y = 4 + 10

Grouping similar terms,

(x + x) + (y - y) = 4 + 10

Solving further,

2x + 0 = 14

x = 14/2

x = 7

Subtracting equation (3) from (4) :-

(x + y) - (x - y) = 10 - 4

Opening brackets,

x + y - x + y = 10 - 4

Grouping similar terms,

(x - x) + (y + y) = 10 - 4

Solving further,

0 + 2y = 6

y = 6/2

y = 3

Answer :-

• x = 7
• y = 3

Answer 2

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